messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-10, -4, 7, 8],\n [10, -7, -8, 6],\n [-7, -3, 2, -2],\n [9, -4, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -27 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-8, 5, 1, 1],\n [0, 11, -7, -4],\n [0, 0, 10, 12],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[8, 1, 8, -12],\n [-3, 8, -10, -3],\n [0, 2, -2, -1],\n [0, 10, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -23 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-4, 10, -9, -2],\n [0, -4, 4, 8],\n [0, 0, -5, -3],\n [0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -60 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -1, 2, -4],\n [-1, -4, 0, -4],\n [2, 0, 5, -4],\n [-4, -4, -4, 0]]\n\nPresent the answer in LaTex f... | 1333 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, -1, 12, 4],\n [-3, 1, 8, 4],\n [8, 11, -7, 11],\n [10, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -2, 0, 5],\n [-2, 0, 0, 7],\n [0, 0, 7, 6],\n [5, 7, 6, 3]]\n\nPresent the answer in LaTex format: \\box... | 30 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 2) rounded to the nearest integer?\n[[-8, -8, 11, -7],\n [-3, -10, 0, 6],\n [4, -10, 12, 12],\n [9, 6, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-7, 7, -12, 5],\n [0, 6, 4, -4],\n [0, 0, 8, 3],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -29 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[12, -8, -2, 3],\n [-8, 4, -2, 2],\n [-2, -2, 2, -8],\n [3, 2, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -19 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 2, 2, -2],\n [0, -1, -4, -2],\n [0, 0, -9, -9],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed... | -96 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[10, 0, -4, -6],\n [0, -2, 8, 4],\n [-4, 8, 1, 0],\n [-6, 4, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 13 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -6, -10, 0],\n [-6, 11, -4, -8],\n [-10, -4, 9, -10],\n [0, -8, -10, -3]]\n\nPresent the answer in LaTex... | -43 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[5, 7, 6, 4],\n [7, -11, 6, -2],\n [6, 6, 0, -3],\n [4, -2, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -78 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, -5, 1, -12],\n [1, 8, 2, 6],\n [-1, 12, 8, -12],\n [-9, -6, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | -221 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -3, -6, -7],\n [0, 10, 4, -9],\n [0, 0, -8, 2],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 185 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, 4, 3, -1],\n [4, -7, 7, -4],\n [3, 7, -1, 4],\n [-1, -4, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, -1, -3, -7],\n [0, -8, 10, -5],\n [0, 0, 1, -6],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 660 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, -11, -7, -9],\n [0, -11, -10, 5],\n [0, 0, -2, 4],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -46 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 3, -3, 5],\n [0, 7, -2, -10],\n [0, 0, -11, 6],\n [0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[-7, -12, -12, 6],\n [1, -11, -9, 6],\n [4, 10, -2, 4],\n [1, 11, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, 2, -11, -3],\n [4, -11, -1, 4],\n [11, -5, 9, -5],\n [8, 6, 5, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 194 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[0, 0, 11, -4],\n [1, -9, 5, -8],\n [3, -8, 6, -7],\n [1, 9, 7, -4]]\n\nPresent the answer ... | 42 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-10, 11, -11, -12],\n [12, -6, -11, 8],\n [-6, -9, -2, 6],\n [4, 2, 1, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13 | MATH |
[
{
"content": "Find the value at position (2, 2) of the inverse of matrix 1/96 * A where A =\n[[2, -12, 4, -5],\n [-12, 11, 2, 8],\n [4, 2, 0, 1],\n [-5, 8, 1, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -7, 1, 7],\n [0, 3, 7, 7],\n [0, 0, -8, -9],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\b... | 17 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[12, 9, -10, -9],\n [0, -9, -1, -9],\n [0, 0, -9, 10],\n [0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -21 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 2, 4, -6],\n [-3, -11, 11, -9],\n [10, 10, 3, 0],\n [-8, -10, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 38 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, 2, 6, 0],\n [2, 8, -7, 6],\n [6, -7, -9, -1],\n [0, 6, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 17 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -10, -10, 11],\n [0, 9, -11, -6],\n [0, 0, -6, 11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex forma... | 11 | MATH |
[
{
"content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[0, 8, -5, 12],\n [-3, -12, -12, 12],\n [-4, -9, 10, -9],\n [0, -5, -3, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 4) rounded to the nearest integer?\n[[4, 3, -4, -4],\n [-1, 5, 12, 3],\n [-5, -10, 11, -9],\n [2, 1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-5, -2, 5, -5],\n [-7, 2, -1, 8],\n [-10, -10, 9, 3],\n [-12, 5, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[4, 6, 8, 6],\n [6, -3, 2, 5],\n [8, 2, 10, -2],\n [6, 5, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, 0, 4, -6],\n [0, 12, 7, -4],\n [4, 7, -4, 0],\n [-6, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -17 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, 7, 6, 6],\n [-6, -8, -9, -2],\n [1, 1, 0, 6],\n [-2, 0, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[5, -11, 6, -8],\n [9, 9, -1, -10],\n [-10, 11, -10, 12],\n [-5, -4, 4, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 241 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[10, -2, 4, 6],\n [0, -6, 12, 3],\n [0, 0, 4, 4],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 6 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 12, 11, 8],\n [0, -12, -1, -11],\n [0, 0, -7, -7],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxe... | -14 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, 3, -1, 3],\n [0, 6, -1, -10],\n [10, 12, -4, -3],\n [11, -12, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-7, 3, -2, 2],\n [-11, -4, -9, 0],\n [0, 12, -7, -8],\n [-11, -9, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{You... | -24 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, 8, -3, -12],\n [12, 5, -4, -3],\n [0, 1, -8, 12],\n [-6, 2, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 5 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 1, -4, -8],\n [1, 5, 9, 2],\n [-4, 9, 2, 6],\n [-8, 2, 6, 11]]\n\nPresent the answer in LaTex forma... | 74 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-7, 8, -2, -8],\n [8, -10, -4, 3],\n [-2, -4, -2, -2],\n [-8, 3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | -18 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[5, -9, 7, -9],\n [0, -2, -11, -3],\n [0, 0, 3, 3],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2298 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -2, 9, 0],\n [-2, -4, 10, -10],\n [9, 10, -1, 10],\n [0, -10, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 18 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 7, 6, 4],\n [7, -3, -5, -3],\n [6, -5, -4, -8],\n [4, -3, -8, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, -1, 0, -2],\n [0, 12, -3, -4],\n [0, 0, 9, -2],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -17 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[10, -5, -5, 4],\n [0, -11, -11, -4],\n [0, 0, -8, -8],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 11, 6, 6],\n [8, 9, -10, -9],\n [-11, 9, -6, 1],\n [-6, -2, 3, -6]]\n\nPresent the answer in LaTex forma... | -9 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[11, 3, -5, -6],\n [-5, 4, -3, 3],\n [-2, 3, -7, -9],\n [2, 4, 9, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-2, -10, 4, -6],\n [-6, -3, 9, -3],\n [6, -3, -9, -3],\n [1, -7, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 334 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-6, -2, -2, -1],\n [-2, -3, 6, -6],\n [-2, 6, -3, -3],\n [-1, -6, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{You... | -14 | MATH |
[
{
"content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[4, -7, 8, 3],\n [-10, 8, -6, -7],\n [11, 2, 8, -1],\n [-1, -8, 11, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[9, 8, 8, 4],\n [8, -1, -6, -2],\n [8, -6, 7, -10],\n [4, -2, -10, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[1, 0, 8, 4],\n [-10, -3, -7, 11],\n [7, 11, 0, 0],\n [-6, -1, 7, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[-1, 0, -2, 0],\n [0, -6, 6, -2],\n [-2, 6, 8, -5],\n [0, -2, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -10 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -12, -4, -1],\n [0, -1, 6, 7],\n [0, -7, 0, 6],\n [-5, 0, -4, -4]]\n\nPresent the answer in LaTex format:... | -44 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[5, 0, 10, 3],\n [-8, -8, -7, 1],\n [-3, -1, 1, 12],\n [-10, 12, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[8, -4, -1, -11],\n [0, 1, -4, -2],\n [0, 0, -10, 1],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 278 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[8, -4, 11, -10],\n [-10, -4, -2, 4],\n [11, 0, -6, 1],\n [12, 8, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 3 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[8, 10, -9, 12],\n [-5, -2, 5, 12],\n [-6, 8, 5, -9],\n [0, 2, -11, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[-12, -2, 1, 12],\n [7, -2, -10, -8],\n [-12, 10, -4, 8],\n [-12, -7, -12, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[5, -1, -6, 0],\n [-1, -9, 2, 8],\n [-6, 2, -6, -5],\n [0, 8, -5, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 8 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-1, 6, 2, 4],\n [6, 2, -10, -1],\n [2, -10, 2, 2],\n [4, -1, 2, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -35664 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[4, 3, 7, -1],\n [0, -1, -5, 6],\n [0, 0, 3, -6],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 680 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-1, 4, -3, -7],\n [0, -12, -4, 9],\n [0, 0, -12, 10],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1133 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -11, -5, 2],\n [0, -8, -3, -10],\n [0, 0, 8, -3],\n [0, 0, 0, -11]]\n\nPresent the an... | -12 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, -11, -3, -9],\n [0, 10, 0, 1],\n [0, 0, -9, 3],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 430 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[12, 4, -4, -6],\n [0, -7, 1, -6],\n [0, 0, -5, 4],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | -19 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[4, 11, -3, 10],\n [1, 10, -6, -4],\n [8, 0, -12, 6],\n [-7, 1, 3, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -44 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 6, 6, 3],\n [6, -5, 0, -5],\n [6, 0, 0, 1],\n [3, -5, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{You... | -40 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[4, -10, -8, 1],\n [6, -12, -11, 7],\n [8, -11, 7, 12],\n [-9, 2, 10, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 124 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, -9, 9, -8],\n [0, 6, 11, 11],\n [0, 0, 11, 2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, -3, 3, 11],\n [3, -4, 4, 4],\n [10, -10, 9, 2],\n [12, 4, 5, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[0, 10, 2, 6],\n [10, -7, 8, 5],\n [2, 8, 1, 4],\n [6, 5, 4, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-8, 3, -4, -5],\n [-4, -7, -1, 10],\n [2, -3, -6, 6],\n [-4, 9, 8, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 44 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -3, 11, -5],\n [-3, -9, -12, 0],\n [-7, -12, 10, -7],\n [9, 11, 1, -9]]\n\nPresent the answer in LaT... | 60 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 2, -3, -12],\n [0, -4, -5, 8],\n [0, 0, -1, -7],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format:... | -158 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -5, 9, -10],\n [-7, -10, -7, -2],\n [-3, 3, -12, 9],\n [6, 11, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{... | 138 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -4, -5, -12],\n [0, -5, -6, 11],\n [0, 0, 11, 12],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex... | 153 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -4, 0, 4],\n [5, 7, -4, -1],\n [-3, -3, -11, 3],\n [-3, -7, -6, 1]]\n\nPresent the answer in LaTex ... | 166 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[8, -5, 4, 9],\n [10, -11, -4, 7],\n [9, -9, -8, -3],\n [7, 8, 4, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 26 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-6, 12, 8, -7],\n [0, -8, -11, 9],\n [0, 0, 11, -2],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -33 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[11, 7, -7, -5],\n [4, 2, 8, 6],\n [5, -2, 2, -1],\n [-10, -3, -11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | -21 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, -8, 0, 0],\n [0, 9, 10, -11],\n [0, 0, -4, -12],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -12, 7, -8],\n [2, -2, -7, -10],\n [3, -8, 9, -10],\n [5, 0, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | -2 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, -9, -8, -10],\n [0, 3, -8, 0],\n [0, 0, 6, -10],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -47 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 5, -5, 6],\n [0, 11, -3, 1],\n [0, 0, 7, -8],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format... | 83 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[7, -10, 6, -8],\n [0, 3, -1, -1],\n [0, 0, -2, -4],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answ... | -48 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, 6, 6, 0],\n [6, 5, -9, -8],\n [6, -9, -7, -2],\n [0, -8, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 17 | MATH |
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[7, 2, -2, -3],\n [2, 6, -12, 0],\n [-2, -12, 2, -1],\n [-3, 0, -1, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-12, 12, 1, -5],\n [6, 2, 2, -2],\n [-10, -9, -11, -4],\n [8, 9, 5, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 385 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[10, 2, -1, 7],\n [-4, -3, -7, -9],\n [11, 6, 9, 12],\n [-10, -6, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -95 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, -2, 2, -6],\n [0, -8, -1, 5],\n [0, 0, -1, 0],\n [0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[1, 1, -1, -7],\n [0, 10, 1, 6],\n [0, 0, -12, 0],\n [0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[8, 0, 12, -5],\n [0, -3, 2, -10],\n [0, 0, -6, -3],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -48 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[8, -11, -7, -7],\n [10, 8, 6, 1],\n [-6, -12, 8, 9],\n [-4, 10, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | -11 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-11, 4, 10, -2],\n [0, -10, -6, -7],\n [0, 0, -1, 0],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -128 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, 12, -11, 0],\n [0, -9, 11, -9],\n [0, 0, -5, 11],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format... | -150 | MATH |
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